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davidrpugh / population-ecology-approach

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Solver generically converging to unstable equilibria #8

Closed davidrpugh closed 10 years ago

davidrpugh commented 10 years ago

I have added a couple of methods for checking the stability of an equilibrium. After solving for the steady state of the model for a given set of parameters and an initial guess, I then compute the eigenvalues of the model Jacobian evaluated at the equilibrium point and checks whether all of the eigenvalues are less than one (in magnitude).

It would seem that the solver generically converges to unstable equilibria (i.e., there is always at least one eigenvalue greater than one. This means, that at least for the moment, the only mechanism we have for finding stable equilibria is to simulate the model from some initial condition.

davidrpugh commented 10 years ago

This issue is no longer relevant given that we have moved to a new prisoner's dilemma payoff matrix where "selfish" females have a higher payoff when they are relatively scarce in the population.